ISCOs and OSCOs in the presence of a positive cosmological constant in massive gravity

TL;DR

This paper investigates how a positive cosmological constant influences the innermost and outermost stable circular orbits in massive gravity, revealing the existence of ISCOs and OSCOs similar to those in Kottler spacetime, with implications across various astrophysical structures.

Contribution

It introduces a detailed analysis of ISCOs and OSCOs in massive gravity with a positive cosmological constant, extending understanding beyond General Relativity and Kottler spacetime.

Findings

Both ISCOs and OSCOs are present in the studied spacetime.

The polynomial for orbit stability is fifth order, allowing numerical root analysis.

Astrophysical structures from atoms to galaxy clusters exhibit these orbits.

Abstract

We study the impact of a non-vanishing (positive) cosmological constant on the innermost and outermost stable circular orbits (ISCOs and OSCOs, respectively) within massive gravity in four dimensions. The gravitational field generated by a point-like object within this theory is known, generalizing the usual Schwarzschild--de Sitter geometry of General Relativity. In the non-relativistic limit, the gravitational potential differs by the one corresponding to the Schwarzschild--de Sitter geometry by a term that is linear in the radial coordinate with some prefactor $\gamma$, which is the only free parameter. Starting from the geodesic equations for massive test particles and the corresponding effective potential, we obtain a polynomial of fifth order that allows us to compute the innermost and outermost stable circular orbits. Next, we numerically compute the real and positive roots of the polynomial for several different structures (from the hydrogen atom to stars and globular clusters to galaxies and galaxy clusters) considering three distinct values of the parameter $\gamma$, determined using physical considerations, such as galaxy rotation curves and orbital precession. Similarly to the Kottler spacetime, both ISCOs and OSCOs appear. Their astrophysical relevance as well as the comparison with the Kottler spacetime are briefly discussed.